How do you simplify #5sqrt2 (sqrt8 - sqrt50)#?

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Answer 1 · 2015-06-06T18:00:50

The simplified writting is #-30#

To simplify, you need to write every term as a multiple of #sqrt2#

#5sqrt2(sqrt8-sqrt50) = 5sqrt2(sqrt(2*4)-sqrt(2*25))#

#= 5sqrt2(sqrt(2*2^2)-sqrt(2*5^2))#

#= 5sqrt2(2sqrt(2)-5sqrt(2))#

#= 5sqrt2*(-3sqrt2)#

#= (5*(-3))*(sqrt2*sqrt2)#

#= -15*2 = -30#